​find the meddian of the following expressions x,= 6,7,5,2,10,9,3        f= 9,12,8,13,11,14,7

Dear Student,

Please find below the solution to the asked query:

First we arrange given data in ascending order and get
 

x	2	3	5	6	7	9	10
f	13	7	8	9	12	14	11	Total = 74

Here , We know : median  = ${\left\{\frac{\mathrm{n} +\hspace{0.17em}1}{2}\right\}}^{\mathrm{th}}$ value , here n = 74  , So

median  = ${\left\{\frac{74 +\hspace{0.17em}1}{2}\right\}}^{\mathrm{th}} = {\left\{\frac{75}{2}\right\}}^{\mathrm{th}}=\mathbf{ }{\left\{\mathbf{37}\mathbf{.}\mathbf{5}\right\}}^{\mathbf{th}}\mathbf{ }\mathbf{value}$

So, The median is the 37.5^th value in the data set

Now to get the median, add up the numbers in the Frequency column until you get to 37 (and since the total number of games is 74, the remaining numbers in that column should also equal 37 ).

And

We will reach 37 after adding  13 + 7 + 8 + 9   = 37 

And  next set of 37 will begin with the frequencies for x  = 7. The median (the 37.5th value) lies between the 37^th value and the 38^th value. Thus, the median lies between x  = 6 and x  = 7.

Now if we calculate the average of these values = $\frac{6 + 7}{2} = \frac{13}{2}$ = 6.5                                       ( Ans )
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